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                <h1 id="第一章：统计学习及监督学习概论"><a href="#第一章：统计学习及监督学习概论" class="headerlink" title="第一章：统计学习及监督学习概论"></a>第一章：统计学习及监督学习概论</h1><h2 id="1-1-统计学习"><a href="#1-1-统计学习" class="headerlink" title="1.1 统计学习"></a>1.1 统计学习</h2><h3 id="1-1-1-统计学习的特点"><a href="#1-1-1-统计学习的特点" class="headerlink" title="1.1.1 统计学习的特点"></a>1.1.1 统计学习的特点</h3><pre><code>统计学习是关于计算机基于数据构建概论统计模型并运用模型对数据进行预测与分析的一门学科，统计学习也称为统计机器学习
另一种观点：统计学习就是计算机系统通过运用数据及统计方法提高系统性能的机器学习。</code></pre><h3 id="1-1-2-统计学习的对象"><a href="#1-1-2-统计学习的对象" class="headerlink" title="1.1.2 统计学习的对象"></a>1.1.2 统计学习的对象</h3><pre><code>统计学习对于数据的基本假设是同类数据具有一定的统计规律性，这是统计学习的前提。</code></pre><h3 id="1-1-3-统计学习的目的"><a href="#1-1-3-统计学习的目的" class="headerlink" title="1.1.3 统计学习的目的"></a>1.1.3 统计学习的目的</h3><pre><code>统计学习用于对数据的预测和分析，特别是对未知数据的预测和分析。</code></pre><h3 id="1-1-4-统计学习的方法"><a href="#1-1-4-统计学习的方法" class="headerlink" title="1.1.4 统计学习的方法"></a>1.1.4 统计学习的方法</h3><pre><code>统计学习的方法是基于数据构建概论统计模型从而对数据进行预测与分析。统计学习方法由监督学习、无监督学习和强化学习组成。
统计学习方法可以概括为：从给定的、有限的、用于学习的训练数据集合出发，假设数据是独立同分布产生的，并且假设要学习的模型属于某个函数的集合，称为假设空间；应用某个评价准则，从假设空间中选取一个最优模型，使其对已知的训练数据及未知的测试数据在给定的评价准则有最优的预测；
统计学习的三要素：模型、策略、算法</code></pre><h2 id="1-2-统计学习的分类"><a href="#1-2-统计学习的分类" class="headerlink" title="1.2 统计学习的分类"></a>1.2 统计学习的分类</h2><h3 id="1-2-1-基本分类"><a href="#1-2-1-基本分类" class="headerlink" title="1.2.1 基本分类"></a>1.2.1 基本分类</h3><pre><code>监督学习：是指从标注数据中学习预测模型的机器学习问题
    其中输入变量和输出变量均为连续变量的预测问题称为 **回归问题**；输出变量为有限个离散变量的预测问题称为 **分类问题**；输入变量与输出变量均为变量序列的预测问题称为**标注问题**。
    监督学习假设输入的变量X和输出的变量Y遵循联合概率分布P(X,Y).其中P(X,Y)表示分布函数或分布密度函数
无监督学习：是指从无标注数据中学习预测模型的机器学习问题。
    无监督学习用于对已有数据的分析，也可以用于对未来数据的预测。
强化学习：是指只能系统在与环境的连续互动中学习最优行为策略的机器学习问题。
半监督学习：是指利用标注数据和未标注数据学习预测模型的机器学习问题。
主动学习：是指机器不断主动给出实例让教师进行标注，然后利用标注数据学习预测模型的机器学习问题。</code></pre><h3 id="1-2-2-按模型分类"><a href="#1-2-2-按模型分类" class="headerlink" title="1.2.2 按模型分类"></a>1.2.2 按模型分类</h3><pre><code>1.概率模型和非概率模型
2.线性模型和非线性模型
3.参数化模型和非参数化模型</code></pre><h3 id="1-2-3-按算法分类"><a href="#1-2-3-按算法分类" class="headerlink" title="1.2.3 按算法分类"></a>1.2.3 按算法分类</h3><pre><code>在线学习：是指每次接受一个样本，进行预测，之后学习模型，并不断重复该操作的机器学习
批量学习：一次接受所有数据，学习模型，之后进行预测。</code></pre><h3 id="1-2-4-按技巧分类"><a href="#1-2-4-按技巧分类" class="headerlink" title="1.2.4 按技巧分类"></a>1.2.4 按技巧分类</h3><pre><code>贝叶斯学习
核方法</code></pre><h2 id="1-3-统计学习方法三要素"><a href="#1-3-统计学习方法三要素" class="headerlink" title="1.3 统计学习方法三要素"></a>1.3 统计学习方法三要素</h2><pre><code>方法 = 模型 + 策略 + 算法</code></pre><h3 id="1-3-2-策略"><a href="#1-3-2-策略" class="headerlink" title="1.3.2 策略"></a>1.3.2 策略</h3><pre><code>损失函数和风险函数
经验风险最小化：经验风险最小的模型就是最优的模型
    当样本容量足够大时，经验风险最小化能保证很好的学习效果，极大似然估计就是经验风险最小化的一个例子。
    但当样本容量很小时，经验风险最小化学习的效果就未必很好，会产生“过拟合”现象。
结构风险最小化：是为了防止过拟合而提出的策略。结构风险最小化等价于正则化。结构风险在经验风险上加上表示模型复杂度的正则化项或罚项。</code></pre><h2 id="1-4-模型评估和模型选择"><a href="#1-4-模型评估和模型选择" class="headerlink" title="1.4 模型评估和模型选择"></a>1.4 模型评估和模型选择</h2><pre><code>泛化：学习方法对未知数据的预测能力
过拟合：指学习时选择的模型所包含的参数过多，以至出现这一模型对已知数据预测得很好，但对未知数据预测得很差的现象。</code></pre><h2 id="1-5-正则化与交叉验证"><a href="#1-5-正则化与交叉验证" class="headerlink" title="1.5 正则化与交叉验证"></a>1.5 正则化与交叉验证</h2><pre><code>模型选择的典型方法是正则化
正则化的作用是选择经验风险与模型复杂度同时较小的模型</code></pre><h3 id="1-5-2-交叉验证"><a href="#1-5-2-交叉验证" class="headerlink" title="1.5.2 交叉验证"></a>1.5.2 交叉验证</h3><pre><code>1.简单交叉验证:首先随机地将一直数据切分成两部分，一部分作为训练集，一部分作为测试集。
2.S这交叉验证：首先随机地将已知数据切分为S个互不相交、大小相同的子集；然后利用S-1个子集的数据训练模型，剩下的子集测试模型；将这一过程对可能的S种选择重复进行；最后选出S次评测中评测测试误差最小的模型。
3.留一交叉验证：S = N</code></pre><h2 id="1-6-泛化能力"><a href="#1-6-泛化能力" class="headerlink" title="1.6 泛化能力"></a>1.6 泛化能力</h2><h2 id="1-7-生成模型与判别模型"><a href="#1-7-生成模型与判别模型" class="headerlink" title="1.7 生成模型与判别模型"></a>1.7 生成模型与判别模型</h2><pre><code>生成方法由数据学习联合概率分布P(X,Y),然后求出条件概率分布P(Y|X)作为预测的模型，即生成模型
判别方法由数据直接学习决策函数f(X)或者条件概率分布P(Y|X)作为预测的模型，即判别模型
生成方法的特点：生成方法可以还原出联合概率分布P(X,Y),而判别方法则不能；生成学习的学习收敛速度更快，即当样本容量增加的时候，学到的模型可以更快地收敛于真实模型；当存在隐变量时，仍可以用生成方法学习，此时判别方法就不能用。
判别方法的特点：判断方法学习的是条件概率P(Y|X)或决策函数f(X),直接面对预测，往往学习的准确率更高；由于直接学习P(Y|X)或f(X)，可以对数据进行各种程度的抽象、定义特征并使用特征，因此可以简化学习问题。</code></pre><h2 id="1-8-监督学习应用"><a href="#1-8-监督学习应用" class="headerlink" title="1.8 监督学习应用"></a>1.8 监督学习应用</h2><h3 id="1-8-1-分类问题"><a href="#1-8-1-分类问题" class="headerlink" title="1.8.1 分类问题"></a>1.8.1 分类问题</h3><pre><code>评价分类器性能的指标一般是分类准确率：对于给定的测试数据集，分类器正确分类的样本数与总样本数之比
精确率：$P = \frac{TP}{TP + FP}$
召回率：$R = \frac{TP}{TP + FN}$
$F_{1}: \frac{1}{F_{1}} = \frac{1}{P} + \frac{1}{R}$</code></pre><h3 id="1-8-2-标注问题"><a href="#1-8-2-标注问题" class="headerlink" title="1.8.2 标注问题"></a>1.8.2 标注问题</h3><h3 id="1-8-3-回归问题"><a href="#1-8-3-回归问题" class="headerlink" title="1.8.3 回归问题"></a>1.8.3 回归问题</h3><script>
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